We study complete approximations of an ontology formulated in a non-Horn description logic (DL) such as $\mathcal{ALC}$ in a Horn DL such as~$\mathcal{EL}$. We provide concrete approximation schemes that are necessarily infinite and observe that in the $\mathcal{ELU}$-to-$\mathcal{EL}$ case finite approximations tend to exist in practice and are guaranteed to exist when the original ontology is acyclic. In contrast, neither of this is the case for $\mathcal{ELU}_\bot$-to-$\mathcal{EL}_\bot$ and for $\mathcal{ALC}$-to-$\mathcal{EL}_\bot$ approximations. We also define a notion of approximation tailored towards ontology-mediated querying, connect it to subsumption-based approximations, and identify a case where finite approximations are guaranteed to exist.
MIPO: Mutual Integration of Patient Journey and Medical Ontology for Healthcare Representation Learning
Australian AI Institute, Faculty of Engineering and IT, University of Technology Sydney（澳大利亚人工智能研究所，工程与信息技术学院，悉尼技术大学）；School of Information Technology and Electrical Engineering, The University of Queensland（信息科技与电气工程学院，昆士兰大学）；Department of Data Science and AI, The Hong Kong Polytechnic University（数据科学与人工智能学院，香港理工大学）；Health Economics and Research Division, Department of Health and Aged Care（健康经济学与研究部，健康与老龄化部）
We study the problem of rewriting an ontology O1 expressed in a DL L1 into an ontology O2 in a Horn DL L2 such that O1 and O2 are equisatisfiable when extended with an arbitrary dataset. Ontologies that admit such rewritings are amenable to reasoning techniques ensuring tractability in data complexity. After showing undecidability whenever L1 extends ALCF, we focus on devising efficiently checkable conditions that ensure existence of a Horn rewriting. By lifting existing techniques for rewriting Disjunctive Datalog programs into plain Datalog to the case of arbitrary first-order programs with …
Rewriting-based approaches for answering queries over an OWL 2 DL ontology have so far been developed mainly for Horn fragments of OWL 2 DL. In this paper, we study the possibilities of answering queries over non-Horn ontologies using datalog rewritings. We prove that this is impossible in general even for very simple ontology languages, and even if PTIME = NP. Furthermore, we present a resolution-based procedure for $\SHI$ ontologies that, in case it terminates, produces a datalog rewriting of the ontology. Our procedure necessarily terminates on DL-Lite_{bool}^H ontologies---an extension of …
We study the problem of rewriting a disjunctive datalog program into plain datalog. We show that a disjunctive program is rewritable if and only if it is equivalent to a linear disjunctive program, thus providing a novel characterisation of datalog rewritability. Motivated by this result, we propose weakly linear disjunctive datalog---a novel rule-based KR language that extends both datalog and linear disjunctive datalog and for which reasoning is tractable in data complexity. We then explore applications of weakly linear programs to ontology reasoning and propose a tractable extension of OWL …
Saarland University（萨尔大学）；University of Freiburg（弗莱堡大学）
State constraints in AI Planning globally restrict the legal environment states. Standard planning languages make closed-domain and closed-world assumptions. Here we address open-world state constraints formalized by planning over a description logic (DL) ontology. Previously, this combination of DL and planning has been investigated for the light-weight DL DL-Lite. Here we propose a novel compilation scheme into standard PDDL with derived predicates, which applies to more expressive DLs and is based on the rewritability of DL queries into Datalog with stratified negation. We also provide a ne…
Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学）
Semantic Web Rule Language (SWRL) combines OWL (Web Ontology Language) ontologies with Horn Logic rules of the Rule Markup Language (RuleML) family. Being supported by ontology editors, rule engines and ontology reasoners, it has become a very popular choice for developing rule-based applications on top of ontologies. However, SWRL is probably not go-ing to become a WWW Consortium standard, prohibiting industrial acceptance. On the other hand, SPIN (SPARQL Inferencing Notation) has become a de-facto industry standard to rep-resent SPARQL rules and constraints on Semantic Web models, building o…
A General Sufficient Condition for Rewriting Horn-ALCHI Atomic Queries into GQL
LIRMM（蒙彼利埃计算机科学、机器人学与微电子实验室）；Inria（法国国家信息与自动化研究所）；University of Montpellier（蒙彼利埃大学）；CNRS（法国国家科学研究中心）；DI ENS（巴黎高等师范学院信息学系）；ENS（巴黎高等师范学院）；PSL University（巴黎文理研究大学）
In many scenarios, complete and incomplete information coexist. For this reason, the knowledge representation and database communities have long shown interest in simultaneously supporting the closed- and the open-world views when reasoning about logic theories. Here we consider the setting of querying possibly incomplete data using logic theories, formalized as the evaluation of an ontology-mediated query (OMQ) that pairs a query with a theory, sometimes called an ontology, expressing background knowledge. This can be further enriched by specifying a set of closed predicates from the theory t…
HSE University（高等经济大学）；Institute for Information Transmission Problems（信息传输问题研究所）；King’s College London（伦敦国王学院）；Steklov Mathematical Institute（斯捷克洛夫数学研究所）；Birkbeck, University of London（伦敦大学伯贝克学院）
Our concern is the problem of efficiently determining the data complexity of answering queries mediated by description logic ontologies and constructing their optimal rewritings to standard database queries. Originated in ontology-based data access and datalog optimisation, this problem is known to be computationally very complex in general, with no explicit syntactic characterisations available. In this article, aiming to understand the fundamental roots of this difficulty, we strip the problem to the bare bones and focus on Boolean conjunctive queries mediated by a simple covering axiom stat…
We study the problem of finite ontology mediated query answering (FOMQA), the variant of OMQA where the represented world is assumed to be finite, and thus only finite models of the ontology are considered. We adopt the most typical setting with unions of conjunctive queries and ontologies expressed in description logics (DLs). The study of FOMQA is relevant in settings that are not finitely controllable. This is the case not only for DLs without the finite model property, but also for those allowing transitive role declarations. When transitive roles are allowed, evaluating queries is challen…
KRDB Research Centre, Free University of Bozen-Bolzano（博岑-博尔扎诺自由大学KRDB研究中心）；Fachbereich Informatik, University of Bremen（不来梅大学计算机系）；Department of Computer Science and Information Systems, Birkbeck, University of London（伦敦大学伯贝克学院计算机科学与信息系统系）；Department of Computer Science, University of Liverpool（利物浦大学计算机系）
We investigate the problem whether two ALC ontologies are indistinguishable (or inseparable) by means of queries in a given signature, which is fundamental for ontology engineering tasks such as ontology versioning, modularisation, update, and forgetting. We consider both knowledge base (KB) and TBox inseparability. For KBs, we give model-theoretic criteria in terms of (finite partial) homomorphisms and products and prove that this problem is undecidable for conjunctive queries (CQs), but 2ExpTime-complete for unions of CQs (UCQs). The same results hold if (U)CQs are replaced by rooted (U)CQs,…
Abductive reasoning generates explanatory hypotheses for new observations using prior knowledge. This paper investigates the use of forgetting, also known as uniform interpolation, to perform ABox abduction in description logic (ALC) ontologies. Non-abducibles are specified by a forgetting signature which can contain concept, but not role, symbols. The resulting hypotheses are semantically minimal and each consist of a set of disjuncts. These disjuncts are each independent explanations, and are not redundant with respect to the background ontology or the other disjuncts, representing a form of…
Building rules on top of ontologies is the ultimate goal of the logical layer of the Semantic Web. To this aim an ad-hoc mark-up language for this layer is currently under discussion. It is intended to follow the tradition of hybrid knowledge representation and reasoning systems such as $\mathcal{AL}$-log that integrates the description logic $\mathcal{ALC}$ and the function-free Horn clausal language \textsc{Datalog}. In this paper we consider the problem of automating the acquisition of these rules for the Semantic Web. We propose a general framework for rule induction that adopts the method…
